Objective 13.1.1: Describe the Photoelectric Effect.
The photoelectric effect is a phenomenon that takes place when the surface of a metal is exposed to monochromatic light, which results in the ejecting of electrons.
Objective 13.1.2: Describe the concept of the photon, and use it to explain the photoelectric effect.
According to the observations made by Max Planck, kinetic energy of a vibrating molecule is quantized and that when radiation is emitted, it is in packets called quantas. From this he derived the relation, E = hf, where E is the energy being carried by a photon, h is the Planck's Constant and f is the frequency of the vibration. According to this energy of a single quantum is proportional to the frequency of the vibration. This tells us that energy is not continuous and can be broken down into discrete packets i.e. quantas.
When Lenard conducted his experiment, he found that the energy of the emitted electrons was independent of the intensity of light that the metal was exposed to, contradictory to Maxwell's theory.
Looking at these 2 observations by Planck and Lenard, Einstein suggested that the incident light was also consisting of quantas and called them Photons. The photons interact with the electrons in the metal as discrete particles in this manner rather than as continuous waves. Taking into consideration the equation E = hf along with Einstein's model of light, energy carried by each photon was proportional to the frequency of the incident light and the Planck's constant and increasing the intensity of light only increased the number of striking photons whereas their energy remained the same. Even if a number of electrons absorbed enough energy from the photons striking them, the average energy stays the same. Hence, the Energy of the emitted electrons is dependent only on the frequency of the photons that hit the metal, even though more maybe ejected as intensity increases.
Objective 13.1.3: Describe and explain an experiment to test the Einstein model.
In Lenard's experiment to detect and measure the photoelectric effect, the apparatus was setup so that light of a specific frequency is shone on a metallic surface resulting in the emission of electrons. A collector plate captures the photoelectrons and the total photoelectric current produced is measured by an ammeter in the circuit. A grid is placed over the emitting surface to create an electric field between the grid and the emitter when a voltage is applied. The voltage can be changed so that the negative retarding potential on the grid is increased until the photoelectrons are no longer detected at the collector. The potential at which photoelectrons are no longer detected is called the stopping potential. Diagrammatical representation of the apparatus is as follows:
Lenard Observed that:
1. Each metal has a certain threshold frequency and no electrons are emitted below this frequency regardless of the intensity of light.
2. More photoelectrons are emitted with greater intensity of light when it has a higher frequency than the threshold frequency.
3. Increase in retarding potential results in decrease in photoelectric current regardless of light intensity.
4. The higher the frequency is of the light falling on the surface, the greater the stopping potential required to stop all photoelectric current.
From all these observations, E = hf can also be said to be hf = Φ + KEmax where Φ is the work function i.e. the energy required for an electron to escape and KEmax is the maximum energy an electron can have. The value of Φ is the product of planck's constant and the threshold frequency and KEmax is the product of the charge on an electron and the stopping potential. Stopping potential can be found by increasing the potential being applied until there is no photoelctric current.
Note from HB: Kinetic energy of the ejected electrons can also be expressed in terms of the stopping potential. In this case, KE = e*V where e is charge of electrons and V is the stopping potential. Using this euqation, hf = Φ + KEmax equation can be written as hf = hfo+eV where fo is threshold frequency.
Objective 13.1.8: Outline a laboratory procedure for producing and observing atomic spectra.
When light is emitted by electrifying a gas in a container, the emitted light can be split into component colors using a prism. It is observed that each different gas has its own type of pattern of line spectrum. The emission spectra tend to be bright lines of different colors (i.e. wavelengths of electromagnetic radiation) that appear against a dark/black background.
In the same way absorption spectra can be observed by shining light through a sample of non-glowing gas and letting the resulting electromagnetic radiation pass through a prism. The light that is emitted after passing through the prism will have several dark bands which have identical postions to those of the bright lines in the emission spectrum for the given element.
The reason that these phenomena take place is because atoms absorb EM waves of a particular frequency and achieve an excited state. They emit EM waves of identical frequencies and return to their ground states.
Objective 13.1.9: Explain how atomic spectra provide evidence for the quantization of energy in atoms.
Two important theories made by Bohr that led to quantum theory of atomic structure were:
1. Electrons travel in circular orbits around the nucleus but only certain orbits are allowed. There is no loss or gain of energy if an electron is in one of these stable orbits, which are called stationary orbits.
2. These orbits have a specific radius and if the radius increases, the energy level of the orbit increases. The smallest orbit (n=1) is the lowest energy level i.e. the ground state of the electron. If an electron moves between energy levels it must gain/lose a specific energy quanta equal to hf, where it is the difference of the initial energy level from the final energy level of the electron. The energy gained or lost is in the form of photons of light.
Note from HB: Limitations of the Bohr Model
1. Model did not predict spectral lines for atoms with two or more electrons
2. did not explain the observed differences in brightness of spectral lines
Objective 13.1.10: Calculate wavelengths of spectral lines from energy level differences and vice versa.
The minimum energy required to completely remove an electron from n=1 to n=∞ is 13.6 eV. Bohr calculated these values for n=∞ to n=2,3,4,5,6 and made a graph similar to the following one:
The energy levels are on the y-axis. The arrows show the levels that an electron can jump to and from. Bohr stated that a quantized photon of light was emitted when an electron jumped from a higher level to a lower level. The energy of this photon can be calculated by the change in the energy of the electron at different energy levels. The difference of the initial energy level from the final energy level is equal to the energy being carried by the photon which is also equal to the product of the frequency of the photon and Planck's constant i.e. hf. In this way values for frequency, the energy of the photon/change in energy of an electron and the jump that an electron has made from one level to another level can be found.
Therefore, through this method, Bohr could predict the line spectrum that is produced by an element by observing the jumps an electron makes from one energy level to another level. However, the limitations to Bohr's method were that the line spectrum for atoms with 2 or more electrons could not be predicted and it did not explain the observed differences between the brightness of the line spectrum.
The photoelectric effect is a phenomenon that takes place when the surface of a metal is exposed to monochromatic light, which results in the ejecting of electrons.
Photo electric effect applet:http://www.ifae.es/xec/phot2.html
Objective 13.1.2: Describe the concept of the photon, and use it to explain the photoelectric effect.
According to the observations made by Max Planck, kinetic energy of a vibrating molecule is quantized and that when radiation is emitted, it is in packets called quantas. From this he derived the relation, E = hf, where E is the energy being carried by a photon, h is the Planck's Constant and f is the frequency of the vibration. According to this energy of a single quantum is proportional to the frequency of the vibration. This tells us that energy is not continuous and can be broken down into discrete packets i.e. quantas.
When Lenard conducted his experiment, he found that the energy of the emitted electrons was independent of the intensity of light that the metal was exposed to, contradictory to Maxwell's theory.
Looking at these 2 observations by Planck and Lenard, Einstein suggested that the incident light was also consisting of quantas and called them Photons. The photons interact with the electrons in the metal as discrete particles in this manner rather than as continuous waves. Taking into consideration the equation E = hf along with Einstein's model of light, energy carried by each photon was proportional to the frequency of the incident light and the Planck's constant and increasing the intensity of light only increased the number of striking photons whereas their energy remained the same. Even if a number of electrons absorbed enough energy from the photons striking them, the average energy stays the same. Hence, the Energy of the emitted electrons is dependent only on the frequency of the photons that hit the metal, even though more maybe ejected as intensity increases.
Objective 13.1.3: Describe and explain an experiment to test the Einstein model.
In Lenard's experiment to detect and measure the photoelectric effect, the apparatus was setup so that light of a specific frequency is shone on a metallic surface resulting in the emission of electrons. A collector plate captures the photoelectrons and the total photoelectric current produced is measured by an ammeter in the circuit. A grid is placed over the emitting surface to create an electric field between the grid and the emitter when a voltage is applied. The voltage can be changed so that the negative retarding potential on the grid is increased until the photoelectrons are no longer detected at the collector. The potential at which photoelectrons are no longer detected is called the stopping potential. Diagrammatical representation of the apparatus is as follows:
Lenard Observed that:
1. Each metal has a certain threshold frequency and no electrons are emitted below this frequency regardless of the intensity of light.
2. More photoelectrons are emitted with greater intensity of light when it has a higher frequency than the threshold frequency.
3. Increase in retarding potential results in decrease in photoelectric current regardless of light intensity.
4. The higher the frequency is of the light falling on the surface, the greater the stopping potential required to stop all photoelectric current.
From all these observations, E = hf can also be said to be hf = Φ + KEmax where Φ is the work function i.e. the energy required for an electron to escape and KEmax is the maximum energy an electron can have. The value of Φ is the product of planck's constant and the threshold frequency and KEmax is the product of the charge on an electron and the stopping potential. Stopping potential can be found by increasing the potential being applied until there is no photoelctric current.
Note from HB: Kinetic energy of the ejected electrons can also be expressed in terms of the stopping potential. In this case, KE = e*V where e is charge of electrons and V is the stopping potential. Using this euqation, hf = Φ + KEmax equation can be written as hf = hfo+eV where fo is threshold frequency.
Objective 13.1.8: Outline a laboratory procedure for producing and observing atomic spectra.
When light is emitted by electrifying a gas in a container, the emitted light can be split into component colors using a prism. It is observed that each different gas has its own type of pattern of line spectrum. The emission spectra tend to be bright lines of different colors (i.e. wavelengths of electromagnetic radiation) that appear against a dark/black background.
In the same way absorption spectra can be observed by shining light through a sample of non-glowing gas and letting the resulting electromagnetic radiation pass through a prism. The light that is emitted after passing through the prism will have several dark bands which have identical postions to those of the bright lines in the emission spectrum for the given element.
The reason that these phenomena take place is because atoms absorb EM waves of a particular frequency and achieve an excited state. They emit EM waves of identical frequencies and return to their ground states.
Objective 13.1.9: Explain how atomic spectra provide evidence for the quantization of energy in atoms.
Two important theories made by Bohr that led to quantum theory of atomic structure were:
1. Electrons travel in circular orbits around the nucleus but only certain orbits are allowed. There is no loss or gain of energy if an electron is in one of these stable orbits, which are called stationary orbits.
2. These orbits have a specific radius and if the radius increases, the energy level of the orbit increases. The smallest orbit (n=1) is the lowest energy level i.e. the ground state of the electron. If an electron moves between energy levels it must gain/lose a specific energy quanta equal to hf, where it is the difference of the initial energy level from the final energy level of the electron. The energy gained or lost is in the form of photons of light.
Note from HB: Limitations of the Bohr Model
1. Model did not predict spectral lines for atoms with two or more electrons
2. did not explain the observed differences in brightness of spectral lines
Objective 13.1.10: Calculate wavelengths of spectral lines from energy level differences and vice versa.
The minimum energy required to completely remove an electron from n=1 to n=∞ is 13.6 eV. Bohr calculated these values for n=∞ to n=2,3,4,5,6 and made a graph similar to the following one:
The energy levels are on the y-axis. The arrows show the levels that an electron can jump to and from. Bohr stated that a quantized photon of light was emitted when an electron jumped from a higher level to a lower level. The energy of this photon can be calculated by the change in the energy of the electron at different energy levels. The difference of the initial energy level from the final energy level is equal to the energy being carried by the photon which is also equal to the product of the frequency of the photon and Planck's constant i.e. hf. In this way values for frequency, the energy of the photon/change in energy of an electron and the jump that an electron has made from one level to another level can be found.
Therefore, through this method, Bohr could predict the line spectrum that is produced by an element by observing the jumps an electron makes from one energy level to another level. However, the limitations to Bohr's method were that the line spectrum for atoms with 2 or more electrons could not be predicted and it did not explain the observed differences between the brightness of the line spectrum.
Sources used:
Class notes
http://www.colorado.edu/physics/2000/quantumzone/photoelectric.html
http://www.physlink.com/Education/AskExperts/ae24.cfm?CFID=13042663&CFTOKEN=74542939
http://spiff.rit.edu/classes/phys314/lectures/photoe/active_chart.gif
http://library.thinkquest.org/28383/grafika/1/afotoelektr1.gif
http://honolulu.hawaii.edu/distance/sci122/Programs/p27/hydrogenspectra.JPG
http://www.physics.udel.edu/~watson/scen103/colloq2000/images/hydrogen.gif